Not sure how much you intend to actually track the car but a heavy car on street tires won't be very satisfying, the heat generated will be more than your street tires are designed to handle. I have friends who swear by Michelin Pilot Super Sports, although on much lighter cars, and the new BFG Rival is getting good reviews in the auto press. If you can't/don't want to spend $ on a set of track wheels/tires the PSS may be a good place to start. Didn't realize it was your DD, when I saw the thread title I thought you were building a hard core track car.
Spend your $ on driver education, that's where the gains are made. You're going to really enjoy getting out on track and learning to drive the ZL1,